Why does time slow down as you reach the speed of light? I.e. If I am in a spaceship going the speed of light?

Answer 1

This is stated in Eintein's Special Theory of Relativity.

It says time is relative with respect to what speed a body is travelling at. It is a really complex theory that is simply impossible to put down in lay man terms so I will just forward you a link.

Many people can give formulae but will not be able to derive how they come about.

Answer 2

Your clock would seem to be running normally to you. If I looked at your clock and the difference between our speeds was close to the light speed, your clock would looks like it was running slow to me and believe it or not, vice versa.